Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid.

We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation, we introduce a dimensionless scalar concentration field ϕ with advective-diffusive dynamics. Activity creates a contribution Σ_{ij}=-κ[over ^][(∂_{i}ϕ)(∂_{j}ϕ)-(∇ϕ)^{2}δ_{ij}/d] to the deviatoric stress, where κ[over ^] is odd under time reversal and d is the number of spatial dimensions; this causes an effective interfacial tension contribution that is negative for contractile swimmers. We predict that domain growth then ceases at a length scale where diffusive coarsening is balanced by active stretching of interfaces, and confirm this numerically. Thus, there is a subtle interplay of activity and hydrodynamics, even without alignment interactions.